On complexity of lobbying in multiple referenda

Christian, Robin; Fellows, Michael R.; Rosamond, Frances A.; Slinko, Arkadii

doi:10.1007/s10058-007-0028-1

Cited by 44 publications

(89 citation statements)

References 13 publications

(11 reference statements)

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“…Thus, there is no hope for fixed-parameter tractability with respect to the parameters s or k . Moreover, a special highlight of our work is to show that even if the gap parameter g (Christian et al, 2007) NP-c). Entries on the main diagonal represent results with respect to single parameters.…”

Section: Our Contributionsmentioning

confidence: 99%

“…Lobbying is NP-complete (Christian et al, 2007). Moreover, in the setting of parameterized complexity analysis (Downey & Fellows, 2013;Flum & Grohe, 2006;Niedermeier, 2006), Christian et al showed that it is W[2]-complete with respect to the parameter "number k of rows to modify", that is, even if only a small number of voters shall be influenced the problem is computationally intractable.…”

Section: Lobbyingmentioning

confidence: 99%

“…Our central point of reference is the work by Christian et al (2007) whose key result is the proof of W[2]-completeness of Lobbying with respect to the number k. Erdélyi, Hemaspaandra, Rothe, and Spakowski (2007) generalized Lobbying to a weighted scenario and showed that an efficient greedy algorithm achieves a logarithmic approximation factor (1 + ln(m · (n + 1)/2 )) for the weighted case. Moreover, they showed that essentially no better approximation ratio can be proven for their algorithm.…”

Section: Related Workmentioning

confidence: 99%

“…A common starting point for each of our SC reductions is to transform S (and U) into a binary matrix in a similar way as Christian et al (2007) transformed Dominating Set instances into binary matrices. The corresponding |S| × |U|-matrix is called SC-matrix and is defined as…”

Section: Set Cover (Sc)mentioning

confidence: 99%

“…While these works relate to campaigning in case of classical voting scenarios where one typically wants to make a specific candidate win or to prevent him from winning, Christian, Fellows, Rosamond, and Slinko (2007) introduced the scenario of lobbying in multiple referenda. Intuitively, the point here is that there are n voters, each of them providing a yes-or no-answer to each of m issues.…”

Section: Introductionmentioning

confidence: 99%

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A Multivariate Complexity Analysis of Lobbying in Multiple Referenda

Bredereck

Hartung

Kratsch

et al. 2014

jair

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Assume that each of n voters may or may not approve each of m issues. If an agent (the lobby) may influence up to k voters, then the central question of the NP-hard Lobbying problem is whether the lobby can choose the voters to be influenced so that as a result each issue gets a majority of approvals. This problem can be modeled as a simple matrix modification problem: Can one replace k rows of a binary n×m-matrix by k all-1 rows such that each column in the resulting matrix has a majority of 1s? Significantly extending on previous work that showed parameterized intractability (W[2]-completeness) with respect to the number k of modified rows, we study how natural parameters such as n, m, k, or the "maximum number of 1s missing for any column to have a majority of 1s" (referred to as "gap value g") govern the computational complexity of Lobbying. Among other results, we prove that Lobbying is fixed-parameter tractable for parameter m and provide a greedy logarithmic-factor approximation algorithm which solves Lobbying even optimally if m ≤ 4. We also show empirically that this greedy algorithm performs well on general instances. As a further key result, we prove that Lobbying is LOGSNP-complete for constant values g ≥ 1, thus providing a first natural complete problem from voting for this complexity class of limited nondeterminism.

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Section: Our Contributionsmentioning

confidence: 99%

Section: Lobbyingmentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

Section: Set Cover (Sc)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A Multivariate Complexity Analysis of Lobbying in Multiple Referenda

Bredereck

Hartung

Kratsch

et al. 2014

jair

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Complexity of Optimal Lobbying in Threshold Aggregation

Nehama

2015

Algorithmic Decision Theory

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Optimal Lobbying is the problem a lobbyist or a campaign manager faces in a full-information voting scenario of a multi-issue referendum when trying to influence the result. The Lobby is faced with a profile that specifies for each voter and each issue whether the voter approves or rejects the issue, and seeks to find the smallest set of voters it must influence to change their vote, for a desired outcome to be obtained. This computational problem also describes problems arising in other scenarios of aggregating complex opinions, such as principal-agents incentives scheme in a complex combinatorial problem, and bribery and manipulation in Truth-Functional Judgement Aggregation. We study the computational complexity of Optimal Lobbying when the issues are aggregated using an anonymous monotone function and the family of desired outcomes is an upward-closed family. We analyze this problem with regard to two parameters: the minimal number of supporters needed to pass an issue, and the size of the maximal minterm of the desired set. We show that for the extreme values of the parameters, the problem is tractable, and provide algorithms. On the other hand, we prove intractability of the problem for the non-extremal values, which are common values for the parameters.

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Parameterized Computational Complexity of Dodgson and Young Elections

Betzler

Guo

Niedermeier

2008

Algorithm Theory – SWAT 2008

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Abstract. We show that, other than for standard complexity theory with known NP-completeness results, the computational complexity of the Dodgson and Young election systems is completely different from a parameterized complexity point of view. That is, on the one hand, we present an efficient fixed-parameter algorithm for determining a Condorcet winner in Dodgson elections by a minimum number of switches in the votes. On the other hand, we prove that the corresponding problem for Young elections, where one has to delete votes instead of performing switches, is W[2]-complete. In addition, we study Dodgson elections that allow ties between the candidates and give fixed-parameter tractability as well as W[2]-hardness results depending on the cost model for switching ties.

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On complexity of lobbying in multiple referenda

Cited by 44 publications

References 13 publications

A Multivariate Complexity Analysis of Lobbying in Multiple Referenda

A Multivariate Complexity Analysis of Lobbying in Multiple Referenda

Complexity of Optimal Lobbying in Threshold Aggregation

Parameterized Computational Complexity of Dodgson and Young Elections

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